This invention relates to an improved method and apparatus for cooling high power microcircuits.
Since the invention of the silicon integrated circuit, there has been in excess of a five orders of magnitude increase in circuit integration (the total number of components on a chip). Part of this increase can be traced to growth in chip size, where the characteristic dimensions have gone from about 1 mm in 1965 to about 4 mm to 8 mm in 1985. The remainder of the increase in circuit integration can be primarily traced to the reduction in the intgrated circuit feature size, which is today generally less than 1.0 .mu.m and rapidly approaching the size of 0.1 .mu.m. In fact, silicon MOSFETs have been made with features as small as 0.025 .mu.m, which is on the order of one hundred atoms across.
The increase in circuit integration continues to be driven by the need for increased processing speed. Processing speed is dependent upon the signal delay times which are directly proportional to the physical length of interconnections between circuit components. A measure of the processing speed is how many millions of instructions per second (MIPS) can be executed. The number of MIPS and the total power dissipation of a chip are both directly proportional to the packaging density. At the component level, the chip power dissipation has been rapidly increasing due to the tremendous increase in the MIPS/chip.
The increase in the chip power dissipation has greatly complicated thermal management of microelectronics. Chips usually must operate at temperatures lower than 120.degree. C. Such a low temperature is dictated by stringent reliability constraints. The failure rate of microelectronic circuitry decreases exponentially with decreasing component temperature. In fact, a commonly used rule of thumb for microelectronic reliability is that a 20.degree. C. decrease in component temperature will typically result in a 50-percent reduction in the failure rate.. Continued pressure to enhance reliability will therefore demand reduction in the component temperatures, as well as more uniform component temperatures.
Forced-convection, liquid cooled, microchannel heat sinks have been recently developed to dissipate heat in modern microcircuitry. The first technical publications on this appeared in the early 1980's as the result of a study done by Tuckerman and Pease at Stanford University, and have caused considerable interest in the heat transfer community.
The configuration of a typical microchannel heat sink is shown in FIG. 1. Heat sink 10 is a finned structure which is cooled by forced convection. The coolant flows from inlet plenum 12 through rectangular microchannels 14, and out into the discharge plenum 16. Power is dissipated by microcircuit 20, and the heat is conducted through the substrate to fins 15 (shown in FIG. 2) where it is conducted to the coolant. The coolant can be either a liquid or a gas, but the pumping power requirements for gases are much larger for the same thermal performance. Also shown in FIG. 1 is cover plate 30 and manifold block 32.
FIG. 2 is a sectional view of the prior art device of FIG. 1 taken along line A--A, and fins 15 can be seen to create microchannels 14 through which the coolant flows. The width of each microchannel is shown as W.sub.c and the width of each fin is shown as W.sub.w. FIG. 3 shows a sectional view of the device of FIG. 1 taken along line B--B. The height of each microchannel is indicated by b, while the distance from circuit 20 and the microchannel is indicated by t. The channel length (or fin length) is indicated in FIG. 1 as L.
The microchannels can be fabricated in silicon substrates by precision sawing or orientation-dependent etching, and usually have a larger height b than width W.sub.c This ratio is called the aspect ratio. The channel width W.sub.c is typically about 55 .mu.m, and the fin thickness W.sub.w is typically about 40 to 45 .mu.m. The substrate height t is typically about 100 to 200 .mu.m, and the fin height b about 300 to 400 .mu.m. The channel length is typically 1.4 to 2.0 cm.
The hydrodynamic and heat transfer properties of flow through the rectangular microchannels depends on the flow regime, which can be laminar, turbulent, or a transitional stage between the two. The parameter used to define the flow regime is the Reynolds number which is given by ##EQU1##
where Re is the Reynolds number, .rho..sub.f the coolant density, .mu..sub.f the coolant dynamic viscosity, V.sub.c the average coolant velocity in the duct, and D.sub.e the hydraulic diameter.
The transition between laminar and turbulent flow occurs over a range of Reynolds numbers. This range is large if the tube entrance is "bell-mouthed" and much smaller if there is an "abrupt" reduction in the flow cross-sectional area at the entrance. In the latter, the flow tends to "trip" at a "critical" Reynolds number, for which the flow is laminar if Re&lt;Re.sub.crit, and the flow is turbulent if Re&gt;Re.sub.crit.
In order to fully understand the design and operation of microchannel heat sinks, the thermal performance of these devices will be analyzed in detail. The thermal performance of a device is often specified in terms of its thermal resistance. The total thermal resistance R is given by R=.DELTA.T/Q, where .DELTA.T is the peak temperature rise above an ambient reference temperature, and Q is the total heating rate. In analyzing microchannel heat sinks, a modified thermal resistance R.sub.tot is used. It is given by ##EQU2## where A.sub.cross is the surface area over which the heat input Q occurs, and q is the heating rate per unit surface area which is assumed to be uniform over A.sub.cross. Using the modified thermal resistance makes it possible to formulate the thermal analysis based on a single channel and an adjacent fin. This is allowed since neighboring channels and fins are symmetrical in thermal response (assuming that the heat source is large enough). Therefore, R.sub.tot will be based on A.sub.cross =L(W.sub.w +W.sub.c).
The total thermal resistance can be thought of as being made up of several components. The arrangement of these thermal resistances is similar to an electrical network of resistors in series and/or parallel. The network will be slightly different depending on the aspect ratio. Six main types of thermal resistance will be discussed next.
The first thermal resistance is R.sub.spread, which is the "constriction resistance" due to thermal spreading from each discrete heat source (e.g., integrated circuit feature or gate) on the surface of the chip. This so-called spreading thermal resistance has been said to be the limiting indicator of transistor speed improvement. This is because the speed of some types of transistors (e.g, bipolar devices) goes up as the supplied power goes up (which is mostly dissipated as heat). Therefore, the transistor speed can be increased only so much because the high heating rate will eventually drive the device temperature too high.
The thermal-spreading resistance will be a function of the size and shape of the heat source. For a circular heat source the following equation can be used: EQU R.sub.spread =.DELTA.T.sub.c /q=1/(2 k.sub.w a.sqroot..pi.)
where a is the radius of the heat source, .DELTA.T.sub.c is the constriction effect, and K.sub.w is the thermal conductivity. For a square heat source the following equation is used: ##EQU3## where k.sub.w is the thermal conductivity of the material evaluated at the device temperature, and a is the characteristic length.
Currently, thermal spreading accounts for on the order of 10.degree. C. of the total temperature rise of about 100.degree. C. in typical silicon chips. However, as the level of circuit integration continues to increase, the temperature rise due to thermal spreading should decrease making this resistance much less significant. Therefore, the effect of thermal spreading will not be included in the thermal resistance models, discussed below.
The second type of thermal resistance is R.sub.solid, which is due to the conduction of heat through the solid material between the heating surface (e.g., integrated circuit) and the fin base and channel base plane. The modified thermal resistance is given by: ##EQU4## where k.sub.w is the wall thermal conductivity evaluated at the average substrate temperature, and t is the substrate thickness. Note that if there is a thermal interface then R.sub.solid will be the sum of the contributions between the heating surface and the interface, and between the interface and the fin base and channel base plane.
The third type of thermal resistance is R.sub.int, which is due to the thermal interface (if any) between the microchannel heat sink and the heat source (e.g., an integrated circuit chip). If there is an interface, then the microchannel heat sink may be considered a "cold plate". Attachment of the heat source can be done using various types of bonding (solder, epoxy, etc), thermal grease, gas layers, etc. The thermal resistance models discussed below assume that the microchannel heat sink is manufactured directly into the substrate of the heat source, and therefore do not include R.sub.int.
The fourth type of thermal resistance is R.sub.cont, which is due to the "constriction effect" at the base of the fin (if there is a fin). If fins are used, it is intended that they transfer more heat than if the fin base surface area were exposed directly to the fluid. This necessitates that the heat flow be "funneled" into the base of the fin. The fins act as a long-strip heat sink for which the constriction thermal resistance may be obtained from the following equation: ##EQU5## where k.sub.w is the material thermal conductivity which is evaluated at the average substrate temperature. This equation applies for large aspect-ratio channels. For moderate aspect-ratio channels, some heat is convected from the channel base thereby making the constriction thermal resistance somewhat smaller. Compared to the overall thermal resistance, this reduction is small and therefore will be ignored for simplicity and conservatism. The constriction thermal resistance is zero for small aspect-ratio channels because the fins are used for structural purposes and are assumed to transfer no heat. The fin thickness is assumed to be much smaller than the channel width, and therefore there is also no constriction thermal resistance for the heat flow into the channel base.
The fifth type of thermal resistance is R.sub.conv, which is due to the convection of heat from the channel base and/or the fin. If there is a fin, R.sub.conv also includes the thermal resistance of heat conduction in the fin. Therefore the convective thermal resistance is given by: ##EQU6##
where M=(2h/K.sub.w W.sub.w).sup.0.5, A.sub.bc is the area of the channel base (LW.sub.c), A.sub.bf is the area of the fin base (LW.sub.w), h is the average heat transfer coefficient, and b is the height of the fin. Using the definition of the fin efficiency, n.sub.f =[tanh(mb)]/mb, and doing some rearranging gives: ##EQU7## which represents the convective thermal resistance between the fin base and channel base plane and the local coolant, for moderate aspect-ratio channels. This equation assumes that the temperatures of the fin base and the channel base are equal. Note that for large aspect-ratio ducts, hw.sub.c .about.0, and for small aspect-ratio ducts 2hbn.sub.f .about.0.
The overall thermal resistance is based on the difference between the peak chip surface temperature and the inlet coolant temperature. Thus, an effective thermal resistance can be defined which is to be added to the local thermal resistance at a given distance from the channel entrance. Therefore, the sixth type of thermal resistance is R.sub.bulk, which is due to the bulk temperature rise of the coolant from the channel entrance caused by absorption of the heat from the microchannel heat sink. The bulk thermal reistance is given by: ##EQU8## where V is the volumetric flow rate of the coolant per channel, V.sub.c is the velocity of the coolant in the channel, Cp.sub.f is the specific heat, and .rho..sub.f is the coolant density.
There is one phenomenon that cannot be put into the form of a thermal resistance since it is independent of the heating rate. This is the temperature rise of the coolant due to viscous heating. The coolant temperature rises due to the conversion of mechanical energy (fluid pressure) into thermal energy (fluid temperature rise). The temperature rise is defined as .DELTA.T.sub.pump and is given by: EQU .DELTA.T.sub.pump =.DELTA.P/.rho..sub.f Cp.sub.f J
where .DELTA.P is the coolant pressure drop (between the inlet plenum and the channel exit), and J is the mechanical equivalent of heat.
To summarize, the total modified thermal resistance is give by the sum of six thermal resistance terms as: EQU R.sub.tot =R.sub.spread +R.sub.solid +R.sub.int +R.sub.cont +R.sub.conv +R.sub.bulk
R.sub.spread is ignored since it should become small as the level of circuit integration increases, and because it is highly dependent on the transistor technology. R.sub.int is in general not required for integrated circuits and is also ignored. Therefore, the thermal resistance models discussed below will consider the total thermal resistance as being given by: EQU R.sub.tot =R.sub.solid +R.sub.cont +R.sub.conv +R.sub.bulk
Since viscous heating cannot be accounted for using a thermal resistance, the total temperature rise at the channel exit is given by: EQU .DELTA.T.sub.tot =R.sub.tot q+.DELTA.T.sub.pump
where it is implied that R.sub.tot and .DELTA.T.sub.pump are independent of q. To be accurate, the properties must be evaluated at proper average temperatures.
To facilitate comparison between heat sink designs, it is necessary to have a common ambient reference temperature (i.e., the inlet coolant temperature). But this is not enough. It is obvious that different heating rates will result in different average properties of the liquid coolant and the heat sink material as well. Therefore, the total thermal resistance of the same heat sink with the same inlet coolant temperature will be different for different heating rates--especially if a comparison is attempted between very small and very large heating rates. Therefore, when comparing various heat sink designs, the heating rate must also be prescribed.
Thermal resistance models will now be analyzed for various channel aspect ratios (.alpha.=b/W.sub.c). They are large (.alpha.&gt;10), moderate (0.1&lt;.alpha.&lt;10), and small (.alpha.&lt;0.1).
Large aspect-ratio channels have large fin heights. The surface area for convective heat transfer of the channel base is small compared to the surface area of the fins. Therefore, the contribution of the channel base to the overall heat transfer is small and can be ignored even though the channel base surface temperature is on average higher than the fin temperature. Ignoring the contribution of the channel base (hw.sub.c .about.0) in R.sub.conv, gives the following model for the total thermal resistance: ##EQU9## where R.sub.tot,large is the total modified thermal resistance for large aspect-ratio channels.
Moderate aspect-ratio channels have shorter fin heights such that the heat transfer from the channel base is also significant (and therefore not ignored). The total thermal resistance is given by: ##EQU10## where R.sub.tot,moderate is the total modified thermal resistance for moderate aspect-ratio channels.
Small aspect-ratio channels have fins which are primarily used for structural purposes. The fins are small in thickness compared to the channel width (w.sub.w &lt;&lt;w.sub.c), and are very short in height (b&lt;&lt;w.sub.c) Therefore, the contribution of the fins to the overall heat transfer is small and can be ignored. Since w.sub.w &lt;&lt;w.sub.c, it is assumed that w.sub.w .about.0, which results in R.sub.cont .about.0. Therefore, the total thermal resistance is: ##EQU11## where R.sub.tot,small is the total modified thermal resistance for small aspect-ratio ducts.
The analysis performed by D. Tuckerman and R. Pease of Stanford University considered similar thermal resistance formulas and developed an "optimum" design for microchannel heat sinks. Their analysis was the basis for prior art microchannel heat sink designs and every microchannel heat sink built to date has been constructed in accordance with their conclusions. The Tuckerman and Pease analysis is discussed in one or more of the following publications, each of which are incorporated herein by reference: Tuckerman, D. B., 1984, "Heat-Transfer Microstructures for Integrated Circuits", PhD Thesis, Stanford University, Stanford, California; Tuckerman, D. B. and Pease, R. F. W., 1981, "High Performance Heat Sinking for VLSI", IEEE Electron Device Lett. EDL-2, pp. 126-129; Tuckerman, D. B. and Pease, R. F. W., 1981, "Ultrahigh Thermal Conductance Microstructures for Cooling Integrated Circuits", 32nd Electronics Components Conf. Proc., pp. 145-149; Tuckerman, D. B. and Pease, R. F. W., 1982, "Optimized Convective Cooling Using Micromachined Structures", Electrochemical Society Extended Abstract No. 125,82, pp. 197-198; Tuckerman, D. B. and Pease, R. F. W., 1983, "Microcapillary Thermal Interface Technology for VLSI Packaging", Symposium on VLSI Technology, Digest of Technical Papers, pp. 60-61. Background material is also available in Philips, R. J., 1988, "Forced Convection Liquid Cooled Microchannel Heat Sinks", Technical Report 787, Massachusetts Institute of Technology, also incorporated herein by reference. The following is a summary of Tuckerman and Pease's analysis and conclusions.
For large aspect-ratio channels, there is a surface area multiplication factor .delta.=2b/(w.sub.w +w.sub.c) due to the fins Assuming fully developed laminar flow at the channel exit provides the friction factor as f=24/Re=24.mu..sub.f /(.rho..sub.f V.sub.c 2w.sub.c). The Nusselt number is constant for a given channel aspect ratio. The coolant pressure drop is a design constraint and is given by .DELTA.P=4f(L/D.sub.e).rho..sub.f Vc.sup.2 /2gc. Upon substitution into the thermal resistance equation, the following thermal resistance model is obtained: ##EQU12## When .delta. is large, it can be shown that w.sub.w =w.sub.c maximizes n.sub.f (which is less than 1.0 and therefore minimizes R). The surface area enhancement is given by .delta.=(k.sub.w /k.sub.f Nu).sup.0.5 which results in n.sub.f =0.76. With these values for .delta. and n.sub.f substituted into the above equation, the "optimum" channel width is given by taking dR/dw.sub.c =0 which gives: EQU W.sub.c .apprxeq.2.29(.mu..sub.f L.sup.2 k.sub.f Nu/.rho..sub.f Cp.sub.f .DELTA.P).sup.0.25
for which the "optimum" modified thermal resistance is given by: ##EQU13##
As a result of this analysis, prior art microchannel heat sinks are designed to operate with fully developed laminar flow and have channel widths typically less than 100 .mu.m.